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The purpose of the present work is to examine two possibilities; firstly,predicting equivalent sand-grain roughness size $k_s$ based on the roughnessheight probability density function and power spectrum leveraging machinelearning as a regression tool, and secondly, extracting information aboutrelevance of different roughness scales to skin-friction drag by interpretingthe output of the trained data-driven model. The model is an ensemble neuralnetwork consisting of 50 deep neural networks. The data for the training of themodel is obtained from direct numerical simulations (DNSs) of turbulent flow inplane channels over 85 irregular multi-scale roughness samples at frictionReynolds number Re$_\tau=800$. The 85 roughness samples are selected from arepository of 4200 samples, covering a wide parameter space, through an activelearning (AL) framework. The selection is made in several iterations, based onthe informativeness of samples in the repository, quantified by the variance ofENN predictions. This AL framework aims to maximize the generalizability of thepredictions with a certain amount of data. This is examined using threedifferent testing data sets with different types of roughness, including 21surfaces from the literature. The model yields an overall mean error of 5\% to10\% on different testing data sets. Subsequently, a data interpretationtechnique, known as layer-wise relevance propagation, is applied to measure thecontributions of different roughness wave-lengths to the predicted $k_s$.High-pass filtering is then applied to the roughness PS to exclude thewave-numbers identified as drag-irrelevant. The filtered rough surfaces areinvestigated using DNS, and it is demonstrated that, despite significant impactof filtering on the roughness topographical appearance and statistics, theskin-friction coefficient of the original roughness is successfully preserved.

Prediction of equivalent sand-grain size and identification of drag-relevant scales of roughness -- a data driven approach